Question

Find the vector projection of vector v onto vector w given that v = <-5, 6> and w = <4, -7>.

a) -47/10
b) 47/10
c) -53/10
d) 53/10

Answer 1

To find the vector projection of vector v onto vector w, we need to calculate the dot product of the two vectors and the magnitude of vector w, and then use the formula projw v = (v · w / |w|^2) * w.

Step-by-step explanation:

To find the vector projection of vector v onto vector w, we first need to calculate the dot product of the two vectors. The dot product of v and w is v · w = (-5)(4) + (6)(-7) = -20 - 42 = -62.

Next, we need to calculate the magnitude of vector w. The magnitude of w is sqrt((4)^2 + (-7)^2) = sqrt(16 + 49) = sqrt(65).

Finally, the vector projection of v onto w is given by the formula projw v = (v · w / |w|^2) * w. Substituting in the values, we have projw v = (-62 / 65) * <4, -7> = <-248/65, 434/65>.